login
Maximal prime gap q-p encountered from 0 to least prime > n.
3

%I #21 Jun 10 2023 08:10:43

%S 2,2,2,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,6,6,6,6,6,6,6,6,6,6,6,

%T 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,

%U 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8

%N Maximal prime gap q-p encountered from 0 to least prime > n.

%D D. S. Mitrinovic et al., Handbook of Number Theory, Kluwer, 1996, Section VII.22, p. 249.

%H Daniel Forgues, <a href="/A166594/b166594.txt">Table of n, a(n) for n = 0..100000</a>

%H Helmut Maier and Carl Pomerance, <a href="https://doi.org/10.1090/S0002-9947-1990-0972703-X">Unusually large gaps between consecutive primes</a>, Transactions of the American Mathematical Society 322.1 (1990): 201-237.

%e a(0) = 2 since the least prime greater than 0 is 2 (first occurrence of gap 2).

%e a(7) = 4 since the least prime greater than 7 is 11 (first occurrence of gap 4).

%Y Cf. A002386, A063095, A151800, A166597, A327441.

%K nonn

%O 0,1

%A _Daniel Forgues_, Oct 17 2009